Since the introduction of model predictive control (MPC), control practitioners have been faced with the
following question: for what class of processes MPC should be implemented? MPC provides a control sequence
that is optimal in the presence or absence of constraints. However, it requires (i) numerically solving a
constrained optimization problem repeatedly on-line and (ii) an adequately reliable model. Alternatively, one
can implement analytical control, such as proportional−integral−derivative (PID) control and differential
geometric control, which does not require the on-line optimization but generally cannot provide the optimal
performance. This paper presents an answer to the following question: for what class of processes can analytical
control provide control quality that is close to the optimal control quality that MPC can provide? Here, an
analytical controller is defined as the one whose implementation does not require solving a constrained
optimization problem numerically. A measure that quantifies the degradation in the closed-loop performance
of a given process when the process is controlled using analytical control instead of MPC has been defined.
The measure is used to characterize the class of input-constrained processes for which MPC provides
significantly higher control quality; processes with directionality and active input constraints benefit more
from MPC. It is shown that structural information on the characteristic (decoupling) matrix of a process is
often adequate for the characterization. Four input-constrained process examples are considered. On the basis
of structural information on the characteristic matrices of the four processes, the processes that can be controlled
satisfactorily using analytical control are specified. Simulated closed-loop responses are then presented, to
show the validity of the characterization.
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